Abstract
In this paper, we study groups with various chain conditions on f-subnormal subgroups. A subgroup H of a group G is called f-subnormal in G if there is a finite chain of subgroups \(H=H_0\le H_1\le \cdots \le H_n=G \), such that either \(|H_{i+1}: H_i|\) is finite or \(H_i\) is normal in \(H_{i+1}\), for \(0\le i\le n-1\).
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This work was supported by the “National Group for Algebraic and Geometric Structures and their Applications” (GNSAGA-INdAM) and the \(\mathrm{A}_\textsc {D}\text {V-AGTA}\) project of which the second and third authors are members. The first author is also a member of the \(\mathrm{A}_\textsc {D}\text {V-AGTA}\) project. The second author would like to thank the University of Alabama for its hospitality, while part of this work was being done.
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Dixon, M.R., Ferrara, M. & Trombetti, M. Groups Satisfying Chain Conditions on f-Subnormal Subgroups. Mediterr. J. Math. 15, 146 (2018). https://doi.org/10.1007/s00009-018-1190-0
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DOI: https://doi.org/10.1007/s00009-018-1190-0
Keywords
- f-subnormal subgroup
- Minimal condition on f-subnormal subgroups
- Maximal condition on f-subnormal subgroups
- f-Wielandt subgroup